Question

The volumes of two cubes are in the ratio 1 : 27. The ratio of their surface area is

Options

• 1 : 3

• 1 : 8

• 1 : 9

•  1 : 18

Answer 1

1 : 9
Let the edges of the two cubes be a and b.
Then, ratio of their volumes     ${\displaystyle }$
Therefore,

${\displaystyle \frac{{\text{a}}^1}{{\text{b}}^3}=\frac{1}{27}}$

${\displaystyle \Rightarrow {\left(\frac{a}{b}\right)}^3={\left(\frac{1}{3}\right)}^3}$

${\displaystyle \Rightarrow \frac{\text{a}}{\text{b}}\prime =\frac{1}{3}}$        

The ratio of their surface areas ${\displaystyle =\frac{6{\text{a}}^2}{6{\text{b}}^2}}$

Therefore,

${\displaystyle \frac{6{\text{a}}^2}{6b^2}=\frac{\text{a2}}{\text{b2}}}$

${\displaystyle =\frac{1}{9}[\text{since}\frac{\text{a}}{\text{b}}=\frac{1}{5}]}$

${\displaystyle =1:9}$

Hence, the ratio of their surface areas is 1:9.